My worst experience was on a flight from Berlin to Canada stopping through Frankfurt and Chicago. The Lufthansa flight from Berlin was delayed by several hours and it caused me to miss my connecting flight in Frankfurt, and they made me wait for over 10 hours to catch the next one with a 10 Euro food coupon as a compensation. I spent my 10 hours in a McDonald's because I had no cash. My second flight was also delayed, causing me to miss the one in Chicago; they put me in another one again but didn't ship my luggages and after I arrived in Canada I waited for over 2 weeks to get them back.

As for the worst airport I've been to, I would say Kuwait's airport is pretty horrible. Even though there are no-smoking signs everywhere, many people including security guards were smoking all over the place.